Okay, we are given 8180 and 9509. Let's add them up step by step.

Step 1: We'll start by adding the digits 0 & 9 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 8 & 9 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8180 + 9509 = 17689.

